Automated proving for class of triangle geometric inequalities

This paper discussed the automated proving for a class of triangle geometric inequalities with only trigonometric functions.Without new radicals,it firstly transformed the original inequality to a two-variable polynomial one using algebraic method firstly.And then it implemented an algorithm based on cell decomposition and real root isolation to prove the two-variable polynomial inequalities,and the output was readable or could be understood with the help of mathematic software.Experiments show that the above methods can prove an extensive class of geometric inequalities with great difficulty automatically and are much efficient especially for the inequalities with only trigonometric functions.Furthermore,the algorithm is suit for triangle geometric inequalities with arbitrary rational coefficients of interior angles.